Module identification in bipartite and directed networks

Complements and competitors: Examining technological co-diffusion and relatedness on a collaborative coding platform

Diffusive and contagious processes spread in the context of one another in connected populations. Diffusions may be more likely to pass through portions of a network where compatible diffusions are already present. We examine this by incorporating the concept of "relatedness" from the economic complexity literature into a network co-diffusion model. Building on the "product space" concept used in this work, we consider technologies themselves as nodes in "product networks," where edges define relationships between products. Specifically, coding languages on GitHub, an online platform for collaborative coding, are considered. From rates of language co-occurrence in coding projects, we calculate rates of functional cohesion and functional equivalence for each pair of languages. From rates of how individuals adopt and abandon coding languages over time, we calculate measures of complementary diffusion and substitutive diffusion for each pair of languages relative to one another. Consistent with the principle of relatedness, network regression techniques (MR-QAP) reveal strong evidence that functional cohesion positively predicts complementary diffusion. We also find limited evidence that functional equivalence predicts substitutive (competitive) diffusion. Results support the broader finding that functional dependencies between diffusive processes will dictate how said processes spread relative to one another across a population of potential adopters.

Community connectivity and local heterogeneity explain animal species co-occurrences within pond communities

Metacommunity processes have the potential to determine most features of the community structure. However, species diversity has been the dominant focus of studies. Nestedness, modularity and checkerboard distribution of species occurrences are main components of biodiversity organisation. Within communities, these patterns emerge from the interaction between functional diversity, spatial heterogeneity and resource availability. Additionally, the connectivity determines the pool of species for community assembly and, eventually, the pattern of species co-occurrence within communities. Despite the recognised theoretical expectations, the change in occurrence patterns within communities along ecological gradients has seldom been considered. Here, we analyse the spatial occurrence of animal species along sampling units within 18 temporary ponds and its relationship with pond environments and geographic isolation. Isolated ponds presented a nested organisation of species with low spatial segregation-modularity and checkerboard-and the opposite was found for communities with high connectivity. A pattern putatively explained by high functional diversity in ponds with large connectivity and heterogeneity, which determines that species composition tracks changes in microhabitats. On the contrary, nestedness is promoted in dispersal-limited communities with low functional diversity, where microhabitat filters mainly affect richness without spatial replacement between functional groups. Vegetation biomass promotes nestedness, probably due to the observed increase in spatial variance in biomass with the mean biomass. Similarly, the richness of vegetation reduced the spatial segregation of animals within communities. This result may be due to the high plant diversity of the pond that is observed similarly along all sampling units, which promotes the spatial co-occurrence of species at this scale. In the study system, the spatial arrangement of species within communities is related to local drivers as heterogeneity and metacommunity processes by means of dispersal between communities. Patterns of species co-occurrence are interrelated with community biodiversity and species interactions, and consequently with most functional and structural properties of communities. These results indicate that understanding the interplay between metacommunity processes and co-occurrence patterns is probably more important than previously thought to understand biodiversity assembly and functioning.

Contextualizing focal structure analysis in social networks

Focal structures are key sets of individuals who may be responsible for coordinating events, protests, or leading citizen engagement efforts on social media networks. Discovering focal structures that are able to promote online social campaigns is important but complex. Unlike influential individuals, focal structures can affect large-scale complex social processes. In our prior work, we applied a greedy algorithm and bi-level decomposition optimization solution to identify focal structures in social media networks. However, the outcomes lacked a contextual representation of the focal structures that affected interpretability. In this research, we present a novel contextual focal structure analysis (CFSA) model to enhance the discovery and the interpretability of the focal structures to provide the context in terms of the content shared by the focal structures through their communication network. The model utilizes multiplex networks, where one layer is the user network based on mentions, replies, friends, and followers, and the second layer is the hashtag co-occurrence network. The two layers have interconnections based on the user hashtag relations. The model's performance was evaluated on various real-world datasets from Twitter related to COVID-19, the Trump vaccine hashtag, and the Black Lives Matter (BLM) social movement during the 2020–2021 time. The model discovered contextual focal structures (CFS) sets revealed the context regarding individuals’ interests. We then evaluated the model's efficacy using various network structural measures such as the modularity method, network stability, and average clustering coefficient to measure the influence of the CFS sets in the network. Ranking correlation coefficient (RCC) was used to conduct the comparative evaluation with real-world scenarios to find the correlated solutions.

The simple emergence of complex molecular function

At odds with a traditional view of molecular evolution that seeks a descent-with-modification relationship between functional sequences, new functions can emerge de novo with relative ease. At early times of molecular evolution, random polymers could have sufficed for the appearance of incipient chemical activity, while the cellular environment harbours a myriad of proto-functional molecules. The emergence of function is facilitated by several mechanisms intrinsic to molecular organization, such as redundant mapping of sequences into structures, phenotypic plasticity, modularity or cooperative associations between genomic sequences. It is the availability of niches in the molecular ecology that filters new potentially functional proposals. New phenotypes and subsequent levels of molecular complexity could be attained through combinatorial explorations of currently available molecular variants. Natural selection does the rest. This article is part of the theme issue 'Emergent phenomena in complex physical and socio-technical systems: from cells to societies'.

Comparing alternatives to the fixed degree sequence model for extracting the backbone of bipartite projections

Projections of bipartite or two-mode networks capture co-occurrences, and are used in diverse fields (e.g., ecology, economics, bibliometrics, politics) to represent unipartite networks. A key challenge in analyzing such networks is determining whether an observed number of co-occurrences between two nodes is significant, and therefore whether an edge exists between them. One approach, the fixed degree sequence model (FDSM), evaluates the significance of an edge's weight by comparison to a null model in which the degree sequences of the original bipartite network are fixed. Although the FDSM is an intuitive null model, it is computationally expensive because it requires Monte Carlo simulation to estimate each edge's p value, and therefore is impractical for large projections. In this paper, we explore four potential alternatives to FDSM: fixed fill model, fixed row model, fixed column model, and stochastic degree sequence model (SDSM). We compare these models to FDSM in terms of accuracy, speed, statistical power, similarity, and ability to recover known communities. We find that the computationally-fast SDSM offers a statistically conservative but close approximation of the computationally-impractical FDSM under a wide range of conditions, and that it correctly recovers a known community structure even when the signal is weak. Therefore, although each backbone model may have particular applications, we recommend SDSM for extracting the backbone of bipartite projections when FDSM is impractical.

Identifying port maritime communities: application to the Spanish case

The aim of this paper is to detect port maritime communities sharing similar international trade patterns, by a modelisation of maritime traffic using a bipartite weighted network, providing decision-makers the tools to search for alliances or identify their competitors. Our bipartite weighted network considers two different types of nodes: one represents the ports, while the other represents the countries where there are major import/export activity from each port. The freight traffic among both types of nodes is modeled by weighting the volume of product transported. To illustrate the model, the Spanish case is considered, with the data segmented by each type of traffic for a fine tuning. A sort of link prediction is possible, finding for those communities with two or more ports, countries that are part of the same community but with which some ports do not have yet significant traffic. The evolution of the traffics is analyzed by comparing the communities in 2009 and 2019. The set of communities formed by the ports of the Spanish port system can be used to identify global similarities between them, comparing the membership of the different ports in communities for both periods and each type of traffic in particular.

Plant-plant co-occurrences under a complex land-use gradient in a temperate forest

Land-use generates multiple stress factors, and we need to understand their effects on plant-plant interactions to predict the consequences of land-use intensification. The stress-gradient hypothesis predicts that the relative strength of positive and negative interactions changes inversely under increasing environmental stress. However, the outcome of interactions also depends on stress factor's complexity, the scale of analysis, and the role of functional traits in structuring the community. We evaluated plant-plant co-occurrences in a temperate forest, aiming to identify changes in pairwise and network metrics under increasing silvopastoral use intensity. Proportionally, positive co-occurrences were more frequent under high than low use, while negative co-occurrences were more frequent under low than high. Networks of negative co-occurrences showed higher centralization under low use, while networks of positive co-occurrences showed lower modularity and higher centralization under high use. We found a partial relationship between co-occurrences and key functional traits expected to mediate facilitation and competition processes. Our results shows that the stress-gradient hypothesis predicts changes in spatial co-occurrences even when two stress factors interact in a complex way. Networks of negative co-occurrences showed a hierarchical effect of dominant species under low use intensity. But positive co-occurrence network structure partially presented the characteristics expected if the facilitation was an important mechanism characterizing the community under high disturbance intensity. The partial relationship between functional traits and co-occurrences may indicate that other factors besides biotic interactions may be structuring the observed negative spatial associations in temperate Patagonian forests.

Understanding digitally enabled complex networks: a plural granulation based hybrid community detection approach

Purpose

Communities representing groups of agents with similar interests or functions are one of the essential features of complex networks. Finding communities in real-world networks is critical for analyzing complex systems in various areas ranging from collaborative information to political systems. Given the different characteristics of networks and the capability of community detection in handling a plethora of societal problems, community detection methods represent an emerging area of research. Contributing to this field, the authors propose a new community detection algorithm based on the hybridization of node and link granulation.

Design/methodology/approach

The proposed algorithm utilizes a rough set-theoretic concept called closure on networks. Initial sets are constructed by using neighborhood topology around the nodes as well as links and represented as two different categories of granules. Subsequently, the authors iteratively obtain the constrained closure of these sets. The authors use node mutuality and link mutuality as merging criteria for node and link granules, respectively, during the iterations. Finally, the constrained closure subsets of nodes and links are combined and refined using the Jaccard similarity coefficient and a local density function to obtain communities in a binary network.

Findings

Extensive experiments conducted on twelve real-world networks followed by a comparison with state-of-the-art methods demonstrate the viability and effectiveness of the proposed algorithm.

Research limitations/implications

The study also contributes to the ongoing effort related to the application of soft computing techniques to model complex systems. The extant literature has integrated a rough set-theoretic approach with a fuzzy granular model (Kundu and Pal, 2015) and spectral clustering (Huang and Xiao, 2012) for node-centric community detection in complex networks. In contributing to this stream of work, the proposed algorithm leverages the unexplored synergy between rough set theory, node granulation and link granulation in the context of complex networks. Combined with experiments of network datasets from various domains, the results indicate that the proposed algorithm can effectively reveal co-occurring disjoint, overlapping and nested communities without necessarily assigning each node to a community.

Practical implications

This study carries important practical implications for complex adaptive systems in business and management sciences, in which entities are increasingly getting organized into communities (Jacucci et al., 2006). The proposed community detection method can be used for network-based fraud detection by enabling experts to understand the formation and development of fraudulent setups with an active exchange of information and resources between the firms (Van Vlasselaer et al., 2017). Products and services are getting connected and mapped in every walk of life due to the emergence of a variety of interconnected devices, social networks and software applications.

Social implications

The proposed algorithm could be extended for community detection on customer trajectory patterns and design recommendation systems for online products and services (Ghose et al., 2019; Liu and Wang, 2017). In line with prior research, the proposed algorithm can aid companies in investigating the characteristics of implicit communities of bloggers or social media users for their services and products so as to identify peer influencers and conduct targeted marketing (Chau and Xu, 2012; De Matos et al., 2014; Zhang et al., 2016). The proposed algorithm can be used to understand the behavior of each group and the appropriate communication strategy for that group. For instance, a group using a specific language or following a specific account might benefit more from a particular piece of content than another group. The proposed algorithm can thus help in exploring the factors defining communities and confronting many real-life challenges.

Originality/value

This work is based on a theoretical argument that communities in networks are not only based on compatibility among nodes but also on the compatibility among links. Building up on the aforementioned argument, the authors propose a community detection method that considers the relationship among both the entities in a network (nodes and links) as opposed to traditional methods, which are predominantly based on relationships among nodes only.

Community Detection in Large-Scale Bipartite Biological Networks

Networks are useful tools to represent and analyze interactions on a large, or genome-wide scale and have therefore been widely used in biology. Many biological networks-such as those that represent regulatory interactions, drug-gene, or gene-disease associations-are of a bipartite nature, meaning they consist of two different types of nodes, with connections only forming between the different node sets. Analysis of such networks requires methodologies that are specifically designed to handle their bipartite nature. Community structure detection is a method used to identify clusters of nodes in a network. This approach is especially helpful in large-scale biological network analysis, as it can find structure in networks that often resemble a "hairball" of interactions in visualizations. Often, the communities identified in biological networks are enriched for specific biological processes and thus allow one to assign drugs, regulatory molecules, or diseases to such processes. In addition, comparison of community structures between different biological conditions can help to identify how network rewiring may lead to tissue development or disease, for example. In this mini review, we give a theoretical basis of different methods that can be applied to detect communities in bipartite biological networks. We introduce and discuss different scores that can be used to assess the quality of these community structures. We then apply a wide range of methods to a drug-gene interaction network to highlight the strengths and weaknesses of these methods in their application to large-scale, bipartite biological networks.

Overlapping Community Detection of Bipartite Networks Based on a Novel Community Density

Community detection plays an essential role in understanding network topology and mining underlying information. A bipartite network is a complex network with more important authenticity and applicability than a one-mode network in the real world. There are many communities in the network that present natural overlapping structures in the real world. However, most of the research focuses on detecting non-overlapping community structures in the bipartite network, and the resolution of the existing evaluation function for the community structure’s merits are limited. So, we propose a novel function for community detection and evaluation of the bipartite network, called community density D. And based on community density, a bipartite network community detection algorithm DSNE (Density Sub-community Node-pair Extraction) is proposed, which is effective for overlapping community detection from a micro point of view. The experiments based on artificially-generated networks and real-world networks show that the DSNE algorithm is superior to some existing excellent algorithms; in comparison, the community density (D) is better than the bipartite network’s modularity.

Spreader events and the limitations of projected networks for capturing dynamics on multipartite networks

Many systems of scientific interest can be conceptualized as multipartite networks. Examples include the spread of sexually transmitted infections, scientific collaborations, human friendships, product recommendation systems, and metabolic networks. In practice, these systems are often studied after projection onto a single class of nodes, losing crucial information. Here, we address a significant knowledge gap by comparing transmission dynamics on temporal multipartite networks and on their time-aggregated unipartite projections to determine the impact of the lost information on our ability to predict the systems' dynamics. We show that the dynamics of transmission models can be dramatically dissimilar on multipartite networks and on their projections at three levels: final outcome, the magnitude of the variability from realization to realization, and overall shape of the temporal trajectory. We find that the ratio of the number of nodes to the number of active edges over the time-aggregation scale determines the ability of projected networks to capture the dynamics on the multipartite network. Finally, we explore which properties of a multipartite network are crucial in generating synthetic networks that better reproduce the dynamical behavior observed in real multipartite networks.

Integrating Prior Knowledge in Mixed-Initiative Social Network Clustering

We propose a new approach-called PK-clustering-to help social scientists create meaningful clusters in social networks. Many clustering algorithms exist but most social scientists find them difficult to understand, and tools do not provide any guidance to choose algorithms, or to evaluate results taking into account the prior knowledge of the scientists. Our work introduces a new clustering approach and a visual analytics user interface that address this issue. It is based on a process that 1) captures the prior knowledge of the scientists as a set of incomplete clusters, 2) runs multiple clustering algorithms (similarly to clustering ensemble methods), 3) visualizes the results of all the algorithms ranked and summarized by how well each algorithm matches the prior knowledge, 4) evaluates the consensus between user-selected algorithms and 5) allows users to review details and iteratively update the acquired knowledge. We describe our approach using an initial functional prototype, then provide two examples of use and early feedback from social scientists. We believe our clustering approach offers a novel constructive method to iteratively build knowledge while avoiding being overly influenced by the results of often randomly selected black-box clustering algorithms.

Hierarchical clustering of bipartite data sets based on the statistical significance of coincidences

When some 'entities' are related by the 'features' they share they are amenable to a bipartite network representation. Plant-pollinator ecological communities, co-authorship of scientific papers, customers and purchases, or answers in a poll, are but a few examples. Analyzing clustering of such entities in the network is a useful tool with applications in many fields, like internet technology, recommender systems, or detection of diseases. The algorithms most widely applied to find clusters in bipartite networks are variants of modularity optimization. Here, we provide a hierarchical clustering algorithm based on a dissimilarity between entities that quantifies the probability that the features shared by two entities are due to mere chance. The algorithm performance is O(n^{2}) when applied to a set of n entities, and its outcome is a dendrogram exhibiting the connections of those entities. Through the introduction of a 'susceptibility' measure we can provide an 'optimal' choice for the clustering as well as quantify its quality. The dendrogram reveals further useful structural information though-like the existence of subclusters within clusters or of nodes that do not fit in any cluster. We illustrate the algorithm by applying it first to a set of synthetic networks, and then to a selection of examples. We also illustrate how to transform our algorithm into a valid alternative for one-mode networks as well, and show that it performs at least as well as the standard, modularity-based algorithms-with a higher numerical performance. We provide an implementation of the algorithm in python freely accessible from GitHub.

Mapping flows on bipartite networks

Mapping network flows provides insight into the organization of networks, but even though many real networks are bipartite, no method for mapping flows takes advantage of the bipartite structure. What do we miss by discarding this information and how can we use it to understand the structure of bipartite networks better? The map equation models network flows with a random walk and exploits the information-theoretic duality between compression and finding regularities to detect communities in networks. However, it does not use the fact that random walks in bipartite networks alternate between node types, information worth 1 bit. To make some or all of this information available to the map equation, we developed a coding scheme that remembers node types at different rates. We explored the community landscape of bipartite real-world networks from no node-type information to full node-type information and found that using node types at a higher rate generally leads to deeper community hierarchies and a higher resolution. The corresponding compression of network flows exceeds the amount of extra information provided. Consequently, taking advantage of the bipartite structure increases the resolution and reveals more network regularities.

Loss of pollinator specialization revealed by historical opportunistic data: Insights from network-based analysis

We are currently facing a large decline in bee populations worldwide. Who are the winners and losers? Generalist bee species, notably those able to shift their diet to new or alternative floral resources, are expected to be among the least vulnerable to environmental change. However, studies of interactions between bees and plants over large temporal and geographical scales are limited by a lack of historical records. Here, we used a unique opportunistic century-old countrywide database of bee specimens collected on plants to track changes in the plant-bee interaction network over time. In each historical period considered, and using a network-based modularity analysis, we identified some major groups of species interacting more with each other than with other species (i.e. modules). These modules were related to coherent functional groups thanks to an a posteriory trait-based analysis. We then compared over time the ecological specialization of bees in the network by computing their degree of interaction within and between modules. “True” specialist species (or peripheral species) are involved in few interactions both inside and between modules. We found a global loss of specialist species and specialist strategies. This means that bee species observed in each period tended to use more diverse floral resources from different ecological groups over time, highly specialist species tending to enter/leave the network. Considering the role and functional traits of species in the network, combined with a long-term time series, provides a new perspective for the study of species specialization.

Drivers of bat roles in Neotropical seed dispersal networks: abundance is more important than functional traits

While functional traits can facilitate or constrain interactions between pair of species in ecological communities, relative abundances regulate the probabilities of encounter among individuals. However, the relative importance of traits and relative abundances for the role species play in seed dispersion networks remains poorly explored. Here, we analyzed 20 Neotropical seed dispersal networks distributed from Mexico to southeastern Brazil to evaluate how relative abundance and functional traits influence bat species' roles in seed dispersal networks. We tested how bat relative abundance and traits relate to species contribution to between-module (c metric) and within-module connectivity (z metric) and their position and potential to mediate indirect effects between species (betweenness centrality). Our results indicate that relative abundance is the main determinant of the role bats play in the networks, while traits such as aspect ratio show modest yet statistically significant importance in predicting specific roles. Moreover, all seed dispersal networks presented two or three superabundant obligatory frugivore species that interacted with a high number of plants. The modest influence of the functional traits on species' roles is likely related to the low variation of morphological traits related to foraging ecology, which reduces the chances of morphological mismatching between consumers and resources in the system. In this scenario, abundant bats have higher chances of encountering resources and being capable of consuming them which leads such species to play critical roles in the community by acting as module hubs and network connectors.

Recommendation decision-making algorithm for sharing accommodation using probabilistic hesitant fuzzy sets and bipartite network projection

In recent years, with the uninterrupted development of sharing accommodation, it not only caters to the diversified accommodation of tourists, but also takes an active role in expanding employment and entrepreneurship channels, enhancing the income of urban and rural residents, and promoting the revitalization of rural areas. However, with the continuous expansion of the scale of sharing accommodation, it is fairly complicated for users to search appropriate services or information. The decision-making problems become more and more complicated. Hence, a probabilistic hesitant fuzzy recommendation decision-making algorithm based on bipartite network projection is proposed in this paper. First of all, combining the users’ decision-making information and the experts’ evaluation information, a bipartite graph connecting users and alternatives is established. Then, the satisfaction degree of probabilistic hesitant fuzzy element is defined. Besides, the recommended alternative is obtained by the allocation of resources. Finally, a numerical case of Airbnb users is given to illustrate the feasibility and effectiveness of the proposed method.

Applications of Network Analysis in Biomedicine

The abundance of high-throughput data and technical refinements in graph theories have allowed network analysis to become an effective approach for various medical fields. This chapter introduces co-expression, Bayesian, and regression-based network construction methods, which are the basis of network analysis. Various methods in network topology analysis are explained, along with their unique features and applications in biomedicine. Furthermore, we explain the role of network embedding in reducing the dimensionality of networks and outline several popular algorithms used by researchers today. Current literature has implemented different combinations of topology analysis and network embedding techniques, and we outline several studies in the fields of genetic-based disease prediction, drug-target identification, and multi-level omics integration.

Specialization in plant-pollinator networks: insights from local-scale interactions in Glenbow Ranch Provincial Park in Alberta, Canada

Background

The occurrence and frequency of plant–pollinator interactions are acknowledged to be a function of multiple factors, including the spatio-temporal distribution of species. The study of pollination specialization by examining network properties and more recently incorporating predictors of pairwise interactions is emerging as a useful framework, yet integrated datasets combining network structure, habitat disturbance, and phylogenetic information are still scarce.

Results

We found that plant–pollinator interactions in a grassland ecosystem in the foothills of the Rocky Mountains are not randomly distributed and that high levels of reciprocal specialization are generated by biological constraints, such as floral symmetry, pollinator size and pollinator sociality, because these traits lead to morphological or phenological mismatching between interacting species. We also detected that landscape degradation was associated with differences in the network topology, but the interaction webs still maintained a consistently higher number of reciprocal specialization cases than expected. Evidence for the reciprocal evolutionary dependence in visitors (e.g., related pollinators visiting related plants) were weak in this study system, however we identified key species joining clustered units.

Conclusions

Our results indicate that the conserved links with keystone species may provide the foundation for generating local reciprocal specialization. From the general topology of the networks, plant–pollinators interactions in sites with disturbance consisted of generalized nodes connecting modules (i.e., hub and numerous connectors). Vice versa, interactions in less disturbed sites consisted of more specialized and symmetrical connections.

A Validity Index for Fuzzy Clustering Based on Bipartite Modularity

Because traditional fuzzy clustering validity indices need to specify the number of clusters and are sensitive to noise data, we propose a validity index for fuzzy clustering, named CSBM (compactness separateness bipartite modularity), based on bipartite modularity. CSBM enhances the robustness by combining intraclass compactness and interclass separateness and can automatically determine the optimal number of clusters. In order to estimate the performance of CSBM, we carried out experiments on six real datasets and compared CSBM with other six prominent indices. Experimental results show that the CSBM index performs the best in terms of robustness while accurately detecting the number of clusters.

Information Loss in Network Pharmacology

With the advent of increasing computational power and large-scale data acquisition, network analysis has become an attractive tool to study the organisation of complex systems and the interrelation of their constituent entities in various scientific domains. In many cases, relations only occur between entities of two different subsets, thereby forming a bipartite network. Often, the analysis of such bipartite networks involves the consideration of its two monopartite projections in order to focus on each entity subset individually as a means to deduce properties of the underlying original network. Although it is broadly acknowledged that this type of projection is not lossless, the inherent limitations of their interpretability are rarely discussed. In this work, we introduce two approaches for measuring the information loss associated with bipartite network projection. Application to two structurally distinct cases in network pharmacology, namely, drug-target and disease-gene bipartite networks, confirms that the major determinant of information loss is the degree of vertices omitted during the monopartite projection.

Availability of food resources and habitat structure shape the individual-resource network of a Neotropical marsupial

Spatial and temporal variation in networks has been reported in different studies. However, the many effects of habitat structure and food resource availability variation on network structures have remained poorly investigated, especially in individual-based networks. This approach can shed light on individual specialization of resource use and how habitat variations shape trophic interactions.To test hypotheses related to habitat variability on trophic interactions, we investigated seasonal and spatial variation in network structure of four populations of the marsupial Gracilinanus agilis in the highly seasonal tropical savannas of the Brazilian Cerrado.We evaluated such variation with network nestedness and modularity considering both cool-dry and warm-wet seasons, and related such variations with food resource availability and habitat structure (considered in the present study as environmental variation) in four sites of savanna woodland forest.Network analyses showed that modularity (but not nestedness) was consistently lower during the cool-dry season in all G. agilis populations. Our results indicated that nestedness is related to habitat structure, showing that this metric increases in sites with thick and spaced trees. On the other hand, modularity was positively related to diversity of arthropods and abundance of fruits.We propose that the relationship between nestedness and habitat structure is an outcome of individual variation in the vertical space and food resource use by G. agilis in sites with thick and spaced trees. Moreover, individual specialization in resource-rich and population-dense periods possibly increased the network modularity of G. agilis. Therefore, our study reveals that environment variability considering spatial and temporal components is important for shaping network structure of populations.

Multiscale core-periphery structure in a global liner shipping network

Maritime transport accounts for a majority of trades in volume, of which 70% in value is carried by container ships that transit regular routes on fixed schedules in the ocean. In the present paper, we analyse a data set of global liner shipping as a network of ports. In particular, we construct the network of the ports as the one-mode projection of a bipartite network composed of ports and ship routes. Like other transportation networks, global liner shipping networks may have core-periphery structure, where a core and a periphery are groups of densely and sparsely interconnected nodes, respectively. Core-periphery structure may have practical implications for understanding the robustness, efficiency and uneven development of international transportation systems. We develop an algorithm to detect core-periphery pairs in a network, which allows one to find core and peripheral nodes on different scales and uses a configuration model that accounts for the fact that the network is obtained by the one-mode projection of a bipartite network. We also found that most ports are core (as opposed to peripheral) ports and that ports in some countries in Europe, America and Asia belong to a global core-periphery pair across different scales, whereas ports in other countries do not.

Efficient Detection of Communities in Biological Bipartite Networks

Methods to efficiently uncover and extract community structures are required in a number of biological applications where networked data and their interactions can be modeled as graphs, and observing tightly-knit groups of vertices ("communities") can offer insights into the structural and functional building blocks of the underlying network. Classical applications of community detection have largely focused on unipartite networks - i.e., graphs built out of a single type of objects. However, due to increased availability of biological data from various sources, there is now an increasing need for handling heterogeneous networks which are built out of multiple types of objects. In this paper, we address the problem of identifying communities from biological bipartite networks - i.e., networks where interactions are observed between two different types of objects (e.g., genes and diseases, drugs and protein complexes, plants and pollinators, and hosts and pathogens). Toward detecting communities in such bipartite networks, we make the following contributions: i) (metric) we propose a variant of bipartite modularity; ii) (algorithms) we present an efficient algorithm called biLouvain that implements a set of heuristics toward fast and precise community detection in bipartite networks (https://github.com/paolapesantez/biLouvain); and iii) (experiments) we present a thorough experimental evaluation of our algorithm including comparison to other state-of-the-art methods to identify communities in bipartite networks. Experimental results show that our biLouvain algorithm identifies communities that have a comparable or better quality (as measured by bipartite modularity) than existing methods, while significantly reducing the time-to-solution between one and four orders of magnitude.

Cluster-based network proximities for arbitrary nodal subsets

The concept of a cluster or community in a network context has been of considerable interest in a variety of settings in recent years. In this paper, employing random walks and geodesic distance, we introduce a unified measure of cluster-based proximity between nodes, relative to a given subset of interest. The inherent simplicity and informativeness of the approach could make it of value to researchers in a variety of scientific fields. Applicability is demonstrated via application to clustering for a number of existent data sets (including multipartite networks). We view community detection (i.e. when the full set of network nodes is considered) as simply the limiting instance of clustering (for arbitrary subsets). This perspective should add to the dialogue on what constitutes a cluster or community within a network. In regards to health-relevant attributes in social networks, identification of clusters of individuals with similar attributes can support targeting of collective interventions. The method performs well in comparisons with other approaches, based on comparative measures such as NMI and ARI.

Identifying compartments in ecological networks based on energy channels

It has been confirmed in many food webs that the interactions between species are divided into “compartments,” that is, subgroups of highly interacting taxa with few weak interactions between the subgroups. Many of the current methods for detecting compartments in food webs are borrowed from network theory, which do little to improve our understanding of the mechanisms underpinning them. Therefore, a method based on ecological context is needed. Here, we develop a new method for detecting compartments in food webs based on the reliance of each node on energy derived from basal resources (i.e., producers or decomposers). Additional Monte Carlo simulations were conducted to test the significance of the compartmentalization. Further, we applied a food web dynamics model to test whether the effects of permutation would be retained within a single compartment. The proposed method identified significant compartments in 23 of the 28 empirical food webs that were investigated. We further demonstrated that the effects of node removal were significantly higher within compartments than between compartments. Our methods and results emphasize the importance of energy channels in forming food web structures, which sheds light on the mechanisms of self‐organization within food webs.

Identification of regulatory modules in genome scale transcription regulatory networks

Background

In gene regulatory networks, transcription factors often function as co-regulators to synergistically induce or inhibit expression of their target genes. However, most existing module-finding algorithms can only identify densely connected genes but not co-regulators in regulatory networks.

Methods

We have developed a new computational method, CoReg, to identify transcription co-regulators in large-scale regulatory networks. CoReg calculates gene similarities based on number of common neighbors of any two genes. Using simulated and real networks, we compared the performance of different similarity indices and existing module-finding algorithms and we found CoReg outperforms other published methods in identifying co-regulatory genes. We applied CoReg to a large-scale network of Arabidopsis with more than 2.8 million edges and we analyzed more than 2,300 published gene expression profiles to charaterize co-expression patterns of gene moduled identified by CoReg.

Results

We identified three types of modules in the Arabidopsis network: regulator modules, target modules and intermediate modules. Regulator modules include genes with more than 90% edges as out-going edges; Target modules include genes with more than 90% edges as incoming edges. Other modules are classified as intermediate modules. We found that genes in target modules tend to be highly co-expressed under abiotic stress conditions, suggesting this network struture is robust against perturbation.

Conclusions

Our analysis shows that the CoReg is an accurate method in identifying co-regulatory genes in large-scale networks. We provide CoReg as an R package, which can be applied in finding co-regulators in any organisms with genome-scale regulatory network data.

Electronic supplementary material

The online version of this article (10.1186/s12918-017-0493-2) contains supplementary material, which is available to authorized users.

Core of communities in bipartite networks

We use the information present in a bipartite network to detect cores of communities of each set of the bipartite system. Cores of communities are found by investigating statistically validated projected networks obtained using information present in the bipartite network. Cores of communities are highly informative and robust with respect to the presence of errors or missing entries in the bipartite network. We assess the statistical robustness of cores by investigating an artificial benchmark network, the coauthorship network, and the actor-movie network. The accuracy and precision of the partition obtained with respect to the reference partition are measured in terms of the adjusted Rand index and the adjusted Wallace index, respectively. The detection of cores is highly precise, although the accuracy of the methodology can be limited in some cases.

Fractal and multifractal analyses of bipartite networks

Bipartite networks have attracted considerable interest in various fields. Fractality and multifractality of unipartite (classical) networks have been studied in recent years, but there is no work to study these properties of bipartite networks. In this paper, we try to unfold the self-similarity structure of bipartite networks by performing the fractal and multifractal analyses for a variety of real-world bipartite network data sets and models. First, we find the fractality in some bipartite networks, including the CiteULike, Netflix, MovieLens (ml-20m), Delicious data sets and (u, v)-flower model. Meanwhile, we observe the shifted power-law or exponential behavior in other several networks. We then focus on the multifractal properties of bipartite networks. Our results indicate that the multifractality exists in those bipartite networks possessing fractality. To capture the inherent attribute of bipartite network with two types different nodes, we give the different weights for the nodes of different classes, and show the existence of multifractality in these node-weighted bipartite networks. In addition, for the data sets with ratings, we modify the two existing algorithms for fractal and multifractal analyses of edge-weighted unipartite networks to study the self-similarity of the corresponding edge-weighted bipartite networks. The results show that our modified algorithms are feasible and can effectively uncover the self-similarity structure of these edge-weighted bipartite networks and their corresponding node-weighted versions.

Network growth models: A behavioural basis for attachment proportional to fitness

Several growth models have been proposed in the literature for scale-free complex networks, with a range of fitness-based attachment models gaining prominence recently. However, the processes by which such fitness-based attachment behaviour can arise are less well understood, making it difficult to compare the relative merits of such models. This paper analyses an evolutionary mechanism that would give rise to a fitness-based attachment process. In particular, it is proven by analytical and numerical methods that in homogeneous networks, the minimisation of maximum exposure to node unfitness leads to attachment probabilities that are proportional to node fitness. This result is then extended to heterogeneous networks, with supply chain networks being used as an example.

Emergence of consensus as a modular-to-nested transition in communication dynamics

Online social networks have transformed the way in which humans communicate and interact, leading to a new information ecosystem where people send and receive information through multiple channels, including traditional communication media. Despite many attempts to characterize the structure and dynamics of these techno-social systems, little is known about fundamental aspects such as how collective attention arises and what determines the information life-cycle. Current approaches to these problems either focus on human temporal dynamics or on semiotic dynamics. In addition, as recently shown, information ecosystems are highly competitive, with humans and memes striving for scarce resources -visibility and attention, respectively. Inspired by similar problems in ecology, here we develop a methodology that allows to cast all the previous aspects into a compact framework and to characterize, using microblogging data, information-driven systems as mutualistic networks. Our results show that collective attention around a topic is reached when the user-meme network self-adapts from a modular to a nested structure, which ultimately allows minimizing competition and attaining consensus. Beyond a sociological interpretation, we explore such resemblance to natural mutualistic communities via well-known dynamics of ecological systems.

Multilayer Network Analysis of Nuclear Reactions

The nuclear reaction network is usually studied via precise calculation of differential equation sets, and much research interest has been focused on the characteristics of nuclides, such as half-life and size limit. In this paper, however, we adopt the methods from both multilayer and reaction networks, and obtain a distinctive view by mapping all the nuclear reactions in JINA REACLIB database into a directed network with 4 layers: neutron, proton, (4)He and the remainder. The layer names correspond to reaction types decided by the currency particles consumed. This combined approach reveals that, in the remainder layer, the β-stability has high correlation with node degree difference and overlapping coefficient. Moreover, when reaction rates are considered as node strength, we find that, at lower temperatures, nuclide half-life scales reciprocally with its out-strength. The connection between physical properties and topological characteristics may help to explore the boundary of the nuclide chart.

The Double-Stranded DNA Virosphere as a Modular Hierarchical Network of Gene Sharing

Virus genomes are prone to extensive gene loss, gain, and exchange and share no universal genes. Therefore, in a broad-scale study of virus evolution, gene and genome network analyses can complement traditional phylogenetics. We performed an exhaustive comparative analysis of the genomes of double-stranded DNA (dsDNA) viruses by using the bipartite network approach and found a robust hierarchical modularity in the dsDNA virosphere. Bipartite networks consist of two classes of nodes, with nodes in one class, in this case genomes, being connected via nodes of the second class, in this case genes. Such a network can be partitioned into modules that combine nodes from both classes. The bipartite network of dsDNA viruses includes 19 modules that form 5 major and 3 minor supermodules. Of these modules, 11 include tailed bacteriophages, reflecting the diversity of this largest group of viruses. The module analysis quantitatively validates and refines previously proposed nontrivial evolutionary relationships. An expansive supermodule combines the large and giant viruses of the putative order "Megavirales" with diverse moderate-sized viruses and related mobile elements. All viruses in this supermodule share a distinct morphogenetic tool kit with a double jelly roll major capsid protein. Herpesviruses and tailed bacteriophages comprise another supermodule, held together by a distinct set of morphogenetic proteins centered on the HK97-like major capsid protein. Together, these two supermodules cover the great majority of currently known dsDNA viruses. We formally identify a set of 14 viral hallmark genes that comprise the hubs of the network and account for most of the intermodule connections.

IMPORTANCE

Viruses and related mobile genetic elements are the dominant biological entities on earth, but their evolution is not sufficiently understood and their classification is not adequately developed. The key reason is the characteristic high rate of virus evolution that involves not only sequence change but also extensive gene loss, gain, and exchange. Therefore, in the study of virus evolution on a large scale, traditional phylogenetic approaches have limited applicability and have to be complemented by gene and genome network analyses. We applied state-of-the art methods of such analysis to reveal robust hierarchical modularity in the genomes of double-stranded DNA viruses. Some of the identified modules combine highly diverse viruses infecting bacteria, archaea, and eukaryotes, in support of previous hypotheses on direct evolutionary relationships between viruses from the three domains of cellular life. We formally identify a set of 14 viral hallmark genes that hold together the genomic network.

Human Impacts and Climate Change Influence Nestedness and Modularity in Food-Web and Mutualistic Networks

Theoretical studies have indicated that nestedness and modularity—non-random structural patterns of ecological networks—influence the stability of ecosystems against perturbations; as such, climate change and human activity, as well as other sources of environmental perturbations, affect the nestedness and modularity of ecological networks. However, the effects of climate change and human activities on ecological networks are poorly understood. Here, we used a spatial analysis approach to examine the effects of climate change and human activities on the structural patterns of food webs and mutualistic networks, and found that ecological network structure is globally affected by climate change and human impacts, in addition to current climate. In pollination networks, for instance, nestedness increased and modularity decreased in response to increased human impacts. Modularity in seed-dispersal networks decreased with temperature change (i.e., warming), whereas food web nestedness increased and modularity declined in response to global warming. Although our findings are preliminary owing to data-analysis limitations, they enhance our understanding of the effects of environmental change on ecological communities.

Efficient community detection of network flows for varying Markov times and bipartite networks

Community detection of network flows conventionally assumes one-step dynamics on the links. For sparse networks and interest in large-scale structures, longer timescales may be more appropriate. Oppositely, for large networks and interest in small-scale structures, shorter timescales may be better. However, current methods for analyzing networks at different timescales require expensive and often infeasible network reconstructions. To overcome this problem, we introduce a method that takes advantage of the inner workings of the map equation and evades the reconstruction step. This makes it possible to efficiently analyze large networks at different Markov times with no extra overhead cost. The method also evades the costly unipartite projection for identifying flow modules in bipartite networks.

Anthropogenic effects are associated with a lower persistence of marine food webs

Marine coastal ecosystems are among the most exposed to global environmental change, with reported effects on species biomass, species richness and length of trophic chains. By combining a biologically informed food-web model with information on anthropogenic influences in 701 sites across the Caribbean region, we show that fishing effort, human density and thermal stress anomaly are associated with a decrease in local food-web persistence. The conservation status of the site, in turn, is associated with an increase in food-web persistence. Some of these associations are explained through effects on food-web structure and total community biomass. Our results unveil a hidden footprint of human activities. Even when food webs may seem healthy in terms of the presence and abundance of their constituent species, they may be losing the capacity to withstand further environmental degradation.

Human activity is affecting the diversity and abundance of marine organisms. Here, Gilarranz et al. show that the persistence of marine food webs is reduced by the effects of fishing pressure, human density, and thermal stress.

Comprehensive spectral approach for community structure analysis on complex networks

A simple but efficient spectral approach for analyzing the community structure of complex networks is introduced. It works the same way for all types of networks, by spectrally splitting the adjacency matrix into a "unipartite" and a "multipartite" component. These two matrices reveal the structure of the network from different perspectives and can be analyzed at different levels of detail. Their entries, or the entries of their lower-rank approximations, provide measures of the affinity or antagonism between the nodes that highlight the communities and the "gateway" links that connect them together. An algorithm is then proposed to achieve the automatic assignment of the nodes to communities based on the information provided by either matrix. This algorithm naturally generates overlapping communities but can also be tuned to eliminate the overlaps.